Question

From 5 liters of 20% solution of alcohol in water 2 liters of the solution is taken out and 2 liters of water is added to it. So, find the strength of alcohol in the new solution.
A. 12%
B. 15%
C. 16%
D. 18%

Answer 1

Hint: First we will analyze the question and apply the given conditions in the question one by one. We will first remove 2 liters from the total amount and then find out the amount of alcohol already present by finding 20% of the remaining solution. After adding 2 liters of water, again we will find the amount of alcohol in the final solution.

Complete step-by-step solution
It is given that there is a total of 5 liters of solution and we are given that 2 liters of the solution are taken out. Therefore, the remaining solution is \[5-2=3\] liters.
Now, it is given that there is 20% alcohol in the solution since there are 3 liters of solution. Therefore, the amount of alcohol in 3 litres solution: $\dfrac{20}{100}\times 3=\dfrac{3}{5}$ litres.
Now, after adding 2 liters of water again, the amount of solution becomes 5 liters again but with different strengths. Now, we have 5 liters of the solution in which $\dfrac{3}{5}$ liter is alcohol:
So, now the percentage of alcohol in 5 litre solution is as follows: $\dfrac{\dfrac{3}{5}}{5}\times 100\Rightarrow \dfrac{3}{5}\times \dfrac{100}{5}=\dfrac{300}{25}=12$
Therefore, the strength of alcohol in the new solution is 12%.
Hence, the correct answer is A.

Note: Remember that while finding the percentage we use the formula: $\dfrac{\text{Amount of alcohol}}{\text{Total amount of solution}}\times 100$ . Always, put a percentage sign at the end every time you use it to show it. A common mistake made is we sometimes forget to mention the unit so always do mention it.